Fixed-time control with prescribed performance for path following of underwater gliders

TL;DR

The paper addresses robust 3D path following for underwater gliders operating in dynamic ocean environments with model uncertainties and disturbances. It proposes a fixed-time prescribed performance controller (FxTPPC) that embeds a finite-time performance function within a fixed-time framework, augmented by a fixed-time disturbance observer and integrated with iLOS guidance for waypoint tracking. Key contributions include the novel combination of FTPF with FxTC to guarantee convergence within a prescribed time independent of initial conditions, a fixed-time disturbance observer for finite-time disturbance estimation, and demonstrated improvements in tracking accuracy, convergence speed, and reduced control chattering compared with SMC and PPC in simulations. This approach enhances robustness and energy efficiency for safe underwater navigation in challenging currents, with potential extensions to 3D waypoint tracking, moving targets, and multi-vehicle formations.

Abstract

Underwater gliders are increasingly deployed in challenging missions - such as hurricane-season observations and long-endurance environmental monitoring - where strong currents and turbulence pose significant risks to navigation safety. To address these practical challenges, this paper presents a fixed-time prescribed performance control scheme for the 3D path following of underwater gliders subject to model uncertainties and environmental disturbances. The primary contribution is the integration of a finite-time performance function within a fixed-time control framework. This synthesis ensures that the tracking errors are constrained within prescribed performance bounds and converge to a compact set within a fixed time, independent of initial conditions. A second key contribution is the development of a fixed-time sliding mode disturbance observer that provides accurate finite-time estimation of lumped disturbances, enhancing the system's robustness. Integrated with an iLOS guidance law, the proposed controller enables precise and safe waypoint following. Numerical simulations demonstrate that the proposed method outperforms conventional sliding mode and prescribed performance controllers in tracking accuracy, convergence speed, and control effort smoothness, validating its efficacy for robust underwater navigation.

Figures (13)

• Figure 1: NED coordinate system for underwater gliders.
• Figure 2: Comparison between the original FTPF and the proposed FTPF used in this work, with the same initial and final values for all functions and the different preset settling times.
• Figure 3: Block diagram of the proposed control system utilizing a fixed-time prescribed performance controller, a fixed-time sliding mode disturbance observer, and an integral LoS guidance law.
• Figure 4: Switching attitude tracking performance comparison among SMC, PPC, and the proposed FxTPPC. In the presence of lumped disturbances, SMC results in large drifting from the reference and PPC leads to high output chattering while FxTPPC is able to track the reference with high accuracy and low oscillation.
• Figure 5: Switching attitude tracking error comparison among SMC, PPC, and the proposed FxTPPC. SMC results in a large drift from the reference attitudes under the influence of disturbances. FxTPPC, compared with PPC, has smoother output tracking and more stable errors around zero.

Theorems & Definitions (15)

• Remark 1
• Definition 2.1
• Definition 2.2
• Lemma 2.3
• Lemma 2.4
• Lemma 2.5
• Remark 2
• Theorem 4.1
• proof
• Remark 3